Subgroups — #16015487

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718725	C₂	1	4	yes	maximal
2	#13123199	C₂	1	1	yes	maximal, characteristic
3	#13114998	C₂	1	4	yes	maximal
4	#13114995	C₂	1	2	yes	maximal
5	#13114992	C₂	1	2	yes	maximal
6	C₄²×#1055	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#125	C₂²	1	2	yes	—
9	C₂×#88124	C₂²	1	2	yes	—
10	C₁₃×#389	—	2	4	no	—
11	C₁₃×#384	C₂²	1	2	yes	—
12	C₁₃×#382	C₂²	1	2	yes	—
13	C₄³×C₁₃	C₂²	1	1	yes	characteristic
14	#11718725	—	2	16	no	—
15	C₂×#88048	C₂²	1	8	yes	—
16	C₂×#88047	C₂²	1	8	yes	—
17	#11718597	C₂²	1	2	yes	—
18	#11718596	C₂²	1	2	yes	—
19	#11718589	—	2	4	no	—
20	C₂×C₄×#1055	C₂²	1	2	yes	—
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
23	C₂×C₄×#1055	C₂²	1	2	yes	—
24	C₁₃×#125	—	2	8	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
28	C₂×C₄²×C₁₃	D₄	1	4	yes	—
29	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₃	—	2	4	no	—
33	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
34	C₂×#6101	—	2	4	no	—
35	C₂²×#1055	C₂³	1	2	yes	—
36	C₂²×#1055	C₂³	1	2	yes	—
37	#88124	—	2	8	no	—
38	C₁₃×#95	—	2	4	no	—
39	#88071	—	2	4	no	—
40	#88048	—	2	16	no	—
41	#88047	—	2	16	no	—
42	C₄×#1055	D₄	1	8	yes	—
43	C₄×#1055	Q₈	1	4	yes	—
44	C₄×#1055	Q₈	1	4	yes	—
45	C₄×#1055	Q₈	1	8	yes	—
46	#33311	—	13	1	no	maximal, Sylow
47	C₂²×C₄×C₁₃	—	2	4	no	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
52	C₂²×Dic₁₃	—	2	4	no	—
53	C₁₃×C₄⋊C₄	—	2	8	no	—
54	C₁₃×C₄⋊C₄	—	4	8	no	—
55	C₁₃×C₄⋊C₄	—	4	8	no	—
56	C₄²×C₁₃	—	2	8	no	—
57	C₄²×C₁₃	C₂×D₄	1	4	yes	—
58	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
59	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
60	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
61	C₄⋊Dic₁₃	—	2	8	no	—
62	C₄⋊Dic₁₃	—	4	8	no	—
63	#6101	—	4	8	no	—
64	C₂×#1055	C₂×D₄	1	4	yes	—
65	C₂×#1055	C₂×D₄	1	4	yes	—
66	C₂×#1055	C₂×Q₈	1	4	yes	—
67	C₂×#1055	C₂×Q₈	1	4	yes	—
68	C₂×#1055	C₂×Q₈	1	4	yes	—
69	C₂×#1055	C₂×Q₈	1	4	yes	—
70	C₂×#499	—	13	4	no	—
71	#2859	—	13	1	no	—
72	#2859	D₁₃	1	1	yes	characteristic
73	#1846	—	13	4	no	—
74	#1845	—	13	2	no	—
75	#1844	—	13	2	no	—
76	C₄²×C₈	—	13	1	no	—
77	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	2	4	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	—	4	8	no	—
82	C₂×C₄×C₁₃	#127	1	4	yes	—
83	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
84	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
85	C₂×C₄×C₁₃	#135	1	8	yes	—
86	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
87	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
90	C₂×Dic₁₃	—	4	4	no	—
91	C₂×Dic₁₃	—	4	8	no	—
92	#1055	C₄⋊Q₈	1	8	yes	—
93	#1055	C₄⋊Q₈	1	8	yes	—
94	C₂×#125	—	13	2	no	—
95	C₂×#125	C₂×D₁₃	1	2	yes	—
96	#499	—	26	16	no	—
97	C₂×#107	—	13	8	no	—
98	C₂×#106	—	13	8	no	—
99	C₂×C₄×C₈	—	13	1	no	—
100	C₂×C₄×C₈	—	13	1	no	—
101	C₂×C₄×C₈	—	13	2	no	—
102	C₂×C₄×C₈	—	13	2	no	—
103	#389	—	2	4	no	—
104	#389	—	26	4	no	—
105	#384	—	13	2	no	—
106	#384	C₂×D₁₃	1	2	yes	—
107	#382	—	13	2	no	—
108	#382	C₂×D₁₃	1	2	yes	—
109	C₄³	C₂×D₁₃	1	1	yes	characteristic
110	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
111	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
112	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
113	C₂²×C₁₃	C₂×#135	1	4	yes	—
114	C₄×C₁₃	—	2	4	no	—
115	C₄×C₁₃	—	2	4	no	—
116	C₄×C₁₃	—	8	4	no	—
117	C₄×C₁₃	#499	1	8	yes	complemented
118	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
119	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
120	Dic₁₃	—	8	4	no	—
121	C₂²×C₈	—	13	2	no	—
122	C₂²×C₈	—	13	2	no	—
123	#125	—	2	8	no	—
124	#125	—	26	8	no	—
125	C₂×C₄⋊C₄	—	2	4	no	—
126	C₂×C₄⋊C₄	—	2	4	no	—
127	C₂×C₄⋊C₄	—	13	4	no	—
128	C₂×C₄⋊C₄	—	26	4	no	—
129	C₂×C₄⋊C₄	—	26	4	no	—
130	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
131	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
132	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
133	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
134	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
135	#107	—	26	16	no	—
136	#106	—	26	16	no	—
137	C₄×C₈	—	13	8	no	—
138	C₄×C₈	—	13	4	no	—
139	C₄×C₈	—	13	4	no	—
140	C₄×C₈	—	13	8	no	—
141	#95	—	2	4	no	—
142	#95	—	26	4	no	—
143	C₂×C₁₃	#2868	1	1	yes	characteristic
144	C₂×C₁₃	#3147	1	2	yes	—
145	C₂×C₁₃	C₂×#499	1	2	yes	—
146	C₂×C₁₃	#3160	1	2	yes	—
147	C₂²×C₄	—	2	4	no	—
148	C₂²×C₄	—	26	4	no	—
149	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
150	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
151	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
152	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
153	C₂×C₈	—	13	4	no	—
154	C₂×C₈	—	13	4	no	—
155	C₂×C₈	—	13	4	no	—
156	C₂×C₈	—	13	4	no	—
157	C₂×C₈	—	13	4	no	—
158	C₂×C₈	—	13	4	no	—
159	C₄⋊C₄	—	2	8	no	—
160	C₄⋊C₄	—	4	8	no	—
161	C₄⋊C₄	—	4	8	no	—
162	C₄⋊C₄	—	26	8	no	—
163	C₄⋊C₄	—	52	8	no	—
164	C₄⋊C₄	—	52	8	no	—
165	C₄²	—	2	8	no	—
166	C₄²	D₄×D₁₃	1	4	yes	—
167	C₄²	Q₈×D₁₃	1	4	yes	—
168	C₄²	Q₈×D₁₃	1	2	yes	—
169	C₄²	Q₈×D₁₃	1	2	yes	—
170	C₁₃	#33311	1	1	yes	characteristic, complemented, Sylow
171	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	4	8	no	—
176	C₂×C₄	—	52	4	no	—
177	C₂×C₄	—	52	8	no	—
178	C₂×C₄	#88194	1	4	yes	—
179	C₂×C₄	#88198	1	4	yes	—
180	C₂×C₄	#88198	1	4	yes	—
181	C₂×C₄	#88204	1	8	yes	—
182	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
183	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
184	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
185	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
186	C₈	—	13	8	no	—
187	C₈	—	13	8	no	—
188	C₂²	C₂×#88194	1	1	yes	characteristic
189	C₂²	C₂×#88198	1	1	yes	characteristic
190	C₂²	C₂×#88198	1	1	yes	characteristic
191	C₂²	C₂×#88204	1	4	yes	—
192	C₄	—	2	4	no	—
193	C₄	—	2	4	no	—
194	C₄	—	8	4	no	—
195	C₄	—	104	4	no	—
196	C₄	#11718725	1	8	yes	complemented
197	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
198	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
199	C₂	#13123232	1	1	yes	characteristic
200	C₂	#13125262	1	2	yes	—
201	C₂	C₂×#11718725	1	2	yes	—
202	C₂	#13125346	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2859	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	#2859	D₁₃
hypocenter	C₁₃	#33311
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
117. C₄×C₁₃	#499	semidirect
170. C₁₃	#33311	semidirect
196. C₄	#11718725	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11718725	2
#13123199	2
#13114998	2
#13114995	2
#13114992	2
C₄²×#1055	2
C₁₃×#2859	2
#33311	13